Finite Group Databasebeta

← #25146158

Subgroups — #25146158

Order 11008.

800 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583119C211yesmaximal, characteristic
2C2×#14583023C211yesmaximal, characteristic, complemented
3#19140080C211yesmaximal, characteristic
4#19139959C211yesmaximal, characteristic, complemented
5#19135979C211yesmaximal, characteristic
6#19135975C211yesmaximal, characteristic, complemented
7#19135916C211yesmaximal, characteristic, complemented
8#19135455C211yesmaximal, characteristic, complemented
9#19135451C211yesmaximal, characteristic
10#19135405C211yesmaximal, characteristic
11#19135362C211yesmaximal, characteristic, complemented
12#19135281C211yesmaximal, characteristic
13#19135272C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#2055C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583119—24no—
21#14583023—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582841—21no—
36#14582827—21no—
37#14582820—21no—
38#14582811—21no—
39#14582806C2211yescharacteristic
40#14582805C2211yescharacteristic
41#14582804C2211yescharacteristic
42#14582802C2211yescharacteristic
43#14582798C2211yescharacteristic
44#14582797C2211yescharacteristic
45#14582792—21no—
46#14582787—21no—
47#14582786—21no—
48#14582782—21no—
49#14582764C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×Dic86C2311yescharacteristic
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063312—22no—
69#13063312—22no—
70Q8×Dic43—22no—
71Q8×Dic43—22no—
72C4×Dic86—22no—
73C4×Dic86—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43D411yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063258—41no—
92#13063257—41no—
93Dic43⋊C8—22no—
94Dic43⋊C8D414yes—
95#13063250—22no—
96#13063250—41no—
97#13063249—22no—
98#13063248—22no—
99#13063246—22no—
100#13063246—22no—
101C4×C43⋊C8—22no—
102C8×Dic43—22no—
103C8×Dic43—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C2×SD16×C43—22no—
118C2×SD16×C43—22no—
119C2×SD16×C43—41no—
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43C2311yescharacteristic
127C4⋊C8×C43—22no—
128#103×C43—22no—
129#102×C43—41no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43#4112yes—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C2×Dic86—22no—
160C2×Dic86—22no—
161C2×Dic86—22no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168SD16×C43—44no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C2×D412yes—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—81no—
181C42×C43—21no—
182C42×C43—21no—
183C22⋊Dic43—42no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—81no—
187#10621885—44no—
188C4⋊Dic43—22no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—42no—
196C4⋊Dic43—42no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—42no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—42no—
203C4×Dic43—81no—
204C4×Dic43C2×D412yes—
205C4×Dic43#4112yes—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8C2×D412yes—
211C2×C43⋊C8#4112yes—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43C22×D411yescharacteristic
220Q8×C43—22no—
221Q8×C43—22no—
222Q8×C43—41no—
223Q8×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43#13512yes—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43#12112yes—
271C2×Dic43#12112yes—
272C2×Dic43#13512yes—
273Dic86—28no—
274Dic86—41no—
275Dic86—41no—
276Dic86—41no—
277Dic86—41no—
278C8×C43—22no—
279C8×C43—41no—
280C43⋊C8—22no—
281C43⋊C8—22no—
282#25297—431nomaximal, Sylow
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43C2×#12111yescharacteristic
291C22×C43#54811yescharacteristic
292C22×C43#55011yescharacteristic
293C22×C43C2×#13511yescharacteristic
294C22×C43C2×#13511yescharacteristic
295C22×C43#57711yescharacteristic
296C22×C43#57811yescharacteristic
297C4×C43—22no—
298C4×C43—42no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43#52911yescharacteristic
303C4×C43#54211yescharacteristic
304C4×C43#54611yescharacteristic
305C4×C43#54811yescharacteristic
306Dic43—22no—
307Dic43—22no—
308Dic43—22no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312Dic43—81no—
313Dic43—81no—
314C2×#464—431no—
315C2×C8×Q8—431no—
316#2592—431no—
317#2581—431no—
318#2067—431no—
319#2066—431no—
320#2056—431no—
321#2055D4311yescharacteristic
322#1969—431no—
323#1968—431no—
324#1958—431no—
325#1949—431no—
326#1934—431no—
327#1933—431no—
328C4×#103—431no—
329C2×C43—161no—
330C2×C43#242611yescharacteristic
331C2×C43#305011yescharacteristic
332C2×C43#306311yescharacteristic
333C2×C43#336411yescharacteristic
334C2×C43#336511yescharacteristic
335C2×C43#339311yescharacteristic
336C2×C43#339411yescharacteristic
337C22×Q16—431no—
338C22×SD16C2×D4311yescharacteristic
339C2×#124—431no—
340C2×C4×Q8—431no—
341C2×C4×Q8—431no—
342#464—864no—
343C8×Q8—864no—
344C2×#107—431no—
345C2×#106—431no—
346C2×C4⋊C8—431no—
347C2×C4⋊C8—431no—
348C2×C4⋊C8C2×D4311yescharacteristic
349C2×#103—431no—
350C2×#103—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103C2×D4311yescharacteristic
354C2×#102—431no—
355C2×#102—431no—
356C2×#102C2×D4311yescharacteristic
357C2×C4×C8—431no—
358C2×C4×C8—431no—
359C2×C4×C8—431no—
360#400—861no—
361#397—861no—
362#395—861no—
363#393—861no—
364#391—431no—
365#391—431no—
366#391—431no—
367#391C2×D4311yescharacteristic
368#390—431no—
369#390C2×D4311yescharacteristic
370#389—431no—
371#389—431no—
372#388—861no—
373#388—861no—
374#387—861no—
375#387—861no—
376#382—431no—
377C4×C4⋊C4—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340C2×D4311yescharacteristic
382C43#2529711yescharacteristic, complemented, Sylow
383C22×Q8—431no—
384C22×Q8—431no—
385C22×Q8C22×D4311yescharacteristic
386C22×D4C22×D4311yescharacteristic
387C2×Q16—862no—
388C2×Q16—862no—
389C2×Q16—1721no—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×SD16—41no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397#124—862no—
398#124—862no—
399C4×Q8—862no—
400C4×Q8—862no—
401C4×Q8—862no—
402C4×Q8—862no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—861no—
423C2×C42—861no—
424C2×C42C22×D4311yescharacteristic
425#107—1721no—
426#106—1721no—
427C4⋊C8—22no—
428C4⋊C8—434no—
429C4⋊C8—862no—
430#103—22no—
431#103—862no—
432#103—862no—
433#103—862no—
434#103—1721no—
435#102—41no—
436#102—862no—
437#102—862no—
438C4×C8—862no—
439C4×C8—862no—
440C4×C8—862no—
441#95—21no—
442#95—21no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—862no—
461C2×Q8—862no—
462C2×Q8—862no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8#1062190012yes—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4D4×D4311yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4C23×D4311yescharacteristic
490Q16—1724no—
491SD16—44no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—432no—
498C2×C8—432no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8D4×D4312yes—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C22⋊C4—42no—
521C22⋊C4—81no—
522C22⋊C4—3441no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C42—21no—
527C42—21no—
528C42—432no—
529C42—432no—
530C42—861no—
531C42—861no—
532C42—3441no—
533C42—1722no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C2×D4×D4311yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546Q8—868no—
547Q8—1721no—
548Q8—1721no—
549Q8—1721no—
550Q8—1721no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—432no—
570C2×C4—432no—
571C2×C4—432no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4#1306334612yes—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4C2×#1062190011yescharacteristic
598C2×C4#1306337011yescharacteristic
599C2×C4#1306337211yescharacteristic
600C8—22no—
601C8—41no—
602C8—862no—
603C8—862no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22#121×D4311yescharacteristic
612C22#1458355511yescharacteristic
613C22#1458356711yescharacteristic
614C22#135×D4311yescharacteristic
615C22C2×#1306334611yescharacteristic
616C22#1458370911yescharacteristic
617C22#1458371511yescharacteristic
618C4—22no—
619C4—41no—
620C4—42no—
621C4—81no—
622C4—81no—
623C4—862no—
624C4—862no—
625C4—862no—
626C4—3441no—
627C4—3441no—
628C4—3441no—
629C4—3441no—
630C4—1721no—
631C4#1458342611yescharacteristic
632C4#1458351711yescharacteristic
633C4#1458353611yescharacteristic
634C4#1458355711yescharacteristic
635C2—161no—
636C2#1913815411yescharacteristic
637C2#1914417111yescharacteristic
638C2#1914428111yescharacteristic
639C2#1914727511yescharacteristic
640C2#1914729511yescharacteristic
641C2#1914758211yescharacteristic
642C2#1914759411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2055C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2055D43
hypocenterC43#25297
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14583023C2semidirect
4. #19139959C2semidirect
6. #19135975C2semidirect
7. #19135916C2semidirect
8. #19135455C2semidirect
11. #19135362C2semidirect
13. #19135272C2semidirect
14. #103×Dic43C2semidirect
382. C43#25297semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145831192
C2×#145830232
#191400802
#191399592
#191359792
#191359752
#191359162
#191354552
#191354512
#191354052
#191353622
#191352812
#191352722
#103×Dic432
C43×#20552
#2529743